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<p>In this section, we show how to use the Laplace transform to solve the one-dimensional heat equation. There are three main steps in order to solve a PDE using the Laplace transform:1. Begin by taking the Laplace transform with one of the two variables, usually <span class="process-math">\(t\text{.}\)</span> This will give an ODE of the transform of the unknown function.2. Solving the ODE, we shall obtain the transform of the unknown function.3. By taking the inverse Laplace transform, we obtain the solution to the original problem.</p>
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